Treatment failure and the threshold of disease extinction - Voottipruex, Pichaya; Patanarapeelert, Nichaphat; Patanarapeelert, Klot (Infectious disease modelling, 2025)
Antibiotic treatment failure related to carriers poses a serious problem to physicians and epidemiologists. Due to the sparsity of data, assessing the role in infection dynamics is difficult. In this study, we examined the possibility that a particular therapeutic effectiveness will be regarded as the disease extinction threshold through the mathematical modelling approach. Including the treatment state in the generic epidemic model with carrier allows us to describe the role of carriers in the treatment failure. The parameterized extinction thresholds were derived via the basic reproduction number for deterministic model, and via the Jury stability criterion for the stochastic model. Existence conditions for the stochastic threshold were derived without the exact formula of the spectral radius of the expectation matrix. The results show that the transmissibility of carrier is necessary for the extinction threshold via treatment failure. The expected extinction threshold may occur subject to the certain range of the transmission potential of the symptomatic infection. This existence conditions are independent of the rate at which the carriers undergo treatment and can be used to support a control strategy. [Display omitted] •Characteristics of antibiotic failure related to carriers were captured through deterministic and stochastic models.•Parametric extinction thresholds were analyzed for both deterministic and stochastic models.•Treatment failure can be a parameterized extinction threshold within a certain range of symptomatic transmissibility.